Something soccer moms often say before, after, or in between swearing, as if to convince someone that they are speaking to that they have picked up a foreign language, and are not just using words like fuck, shit, ass, bitch, or possibly Barbara Steisand.

Excuse my french, but little jason is just the most retarded fucking little bastard on the block. Too bad his fucking whore of a mother didn't use a condom.

French is commonly associated with sexual vulgarity. The idea that anything French is wicked, sexual, and decadent has invited many English speakers to insult the frogs.
The term "French" has many other sexual meanings. French culture is a common sex worker euphemism for oral sex, a French lesson is a visit to a prostitute, French kissing is a more vulgar kind of kissing. They used to call porn pictures "French prints" and being Frenchified was catching syphilis.
Reference: The Slanguage of Sex by Brigid McConville & John Shearlaw, 1985.

Excuse my french, but that guy is such a fucking douche, he tried to dead horse my roommate while she was passed out drunk!

A handy phrase used to cover up a quick outburst of obsanities near children, playing nice with your son/daughter's school principal, a downgrading insultance breakdown for a Mary Sue, or just to impress your new boss at work.

"Excuse my french, but that new girl who is currently trying to fuck her way into getting an A into the new semester, is a half price bargain bin whore and should be shot down with a rabies gun." Said the Punk to the Goth.

The Goth narrowed her eyes, "Maybe the paper boy was right, we will conquer the world with darkness some day."